Problem: Reduce to lowest terms: $- \dfrac{9}{5} \div - \dfrac{9}{2} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{2}$ is $- \dfrac{2}{9}$ Therefore: $ - \dfrac{9}{5} \div - \dfrac{9}{2} = - \dfrac{9}{5} \times - \dfrac{2}{9} $ $ \phantom{- \dfrac{9}{5} \times - \dfrac{2}{9}} = \dfrac{-9 \times -2}{5 \times 9} $ $ \phantom{- \dfrac{9}{5} \times - \dfrac{2}{9}} = \dfrac{18}{45} $ The numerator and denominator have a common divisor of $9$, so we can simplify: $ \dfrac{18}{45} = \dfrac{18 \div 9}{45 \div 9} = \dfrac{2}{5} $